If roots of `x^3+bx^2+cx+d=0` are (A) in A.P. then `2b^3-9bc+27d=0` (B) in GP then `b^3d=c^3` (C) in GP then `27d^3=9bcd^2-4c^3d` (D) equal then `c^3=b^3+3bc`

If the roots of ax^3 + bx^2 + cx +d=0 are in A.P then the roots of a ( x+k)^3 + b ( x + k)^2 + c ( x+k) + d=0 are in

If the zeros of the polynomial f(x)=a x^3+3b x^2+3c x+d are in A.P., prove that 2b^3-3a b c+a^2d=0 .

If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .

The condition that the roots of the equation ax^3+bx^2+cx+d=0 may be in A.P., if (i)2b^3+27a^2d=9abc (ii)2b^3+27a^2d=-9abc (iii) 2b^3-27a^2d=9abc (iv) 2b^3-27a^2d=-9abc

The condition that the roots of the equation ax^3+bx^2+cx+d=0 may be in A.P., if (i) 2b^3+27a^2d=9abc (ii) 2b^3+27a^2d=-9abc (iii) 2b^3-27a^2d=9abc (iv) 2b^3-27a^2d=-9abc

If the roots of the equation x^(3) + bx^(2) + cx + d = 0 are in arithmetic progression, then b, c and d satisfy the relation

If the roots of the equation x^(3) + bx^(2) + cx + d = 0 are in arithmetic progression, then b, c and d satisfy the relation

Let alpha, beta, gamma are the roots of f(x)-=ax^(3)+bx^(2)+cx+d=0 . Then the condition for roots of f(x)=0 are in G.P is (A) ac^(3)=b^(3)d (B) a^(3)c=bd^(3) (C) ac=bd (D) a^(2)c=b^(2)d

If ax^3 + bx^2 + cx + d is divisible by ax^2 + c, then a, b, c, d are in (a) AP (b) GP (c) HP